符号可逆图和平衡图

Signed Invertible Graphs and Balanced Graphs

单图Ｇ是符号可逆图，如果它的邻接矩阵Ａ（Ｇ）的逆矩阵Ａ￣（－１）（Ｇ）是某个符号图Ｈ的邻接矩阵。符号图Ｓ是平衡图，如果它的每一个圈都包含偶数条负边。构造了一类符号可逆图，并给出了这类图的符号逆图是平衡图的充要条件。

Agraph G is called signed invertible if its adjacency matrix A(G)has an inverse A ￣(-1) (G) which is the adjacency matrix of some signed graph H.Asigned graph S is balanced if each of its cycles contains even negative edges. We now construct a class of signed invertible graphs,and obtain the condition of equivalence of their signed inverse graphs′being balanced graphs.